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Simultaneous estimation of first and second derivatives of a cost function

Simultaneous estimation of first and second derivatives of a cost function

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A correlation method for estimating the second derivative, as well as the first derivative, of a cost function which is quadratic in an input parameter is described. The method, using a 3-level msequence perturbation signal, enables the cost-function minimum to be reached in a single step in a noisefree system. The effects of noise, and the extension of the method to multiparameter cost functions, are discussed.

References

    1. 1)
      • van der Grinten, P.M.E.M.: `The application of random test signals in process optimization', Paper 263, 2nd IFAC Congress, 1963, Basle.
    2. 2)
      • Douce, J.L., Ng, K.C.: `The use of pseudorandom binary test signals in process optimization', IFAC symposium on the theory of self-adaptive control systems, September 1965, Teddington, (To be published by the Instrument Society of America).
    3. 3)
      • Clarke, D.W.: `Self-optimizing systems involving the estimation of cost-function slope using pseudorandom binary perturbations', Auto 20, National Physical Laboratory Report, 1966.
    4. 4)
      • K.R. Godfrey . Three-level m sequences. Electronics Letters
    5. 5)
      • P.A.N. Briggs , K.R. Godfrey . Pseudorandom signals for the dynamic analysis of multivariable systems. Proc. IEE , 7
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